Seven Basic Quality Management Tools

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Seven Basic Quality tools documents

Definition of Quality Management -- it is a method for ensuring that all the activities necessary to design, develop and implement a
product or service are effective and efficient with respect to the system and its performance. It is also a principle set by the company
to endure the continuous advocacy of quality services and products, or the further improvement of it.

Welcome to QT-charts knowledge base section.
Hopefully you will find some of them useful in your work. (Read articles below to learn more.)

Demerit Control Charts

Original text on www.freequality.org

A control chart is
an important tool in statistical process control. Control charts provide a way
to see whether a process is in control by being able to see if the process is
within the set upper and lower limits. Control charts were created by Walter
A. Shewart in the 1920’s and then picked up and used widely by W. Edward
Demings.

The demerit control chart
was created by H.F. Dodge while working at Bell Laboratories as a means to
chart products with more than one kind of possible defect. Some defects had
very serious consequences on the performance of the product and some were not very
serious. Dodge classified the various types of defects into four different
categories. Conerly, et al described these different categories as follows:

Class "A" Defects-Very Serious.

-Will render unit totally unfit for service.

-Will surely cause operating failure of the unit in
service which cannot be readily corrected on the job.

-Liable to cause personal injury or property damage.

Class "B" Defects-Serious.

-Will probably, but not surely cause Class "A"
operating failure of the unit in service.

-Will surely cause trouble of a nature less serious than
Class "A"

-Will surely cause increased maintenance or decreased
life.

Class "C" Defects-Moderately Serious.

-Will possibly cause operating failure of the unit in
service. Likely to cause trouble of a nature less serious than operating
failure.

-Likely to cause increased maintenance or decreased
life.

-Major defects of appearance, finish, or workmanship.

Class "D" Defects-Not Serious.

-Will not cause operating failure of the unit in
service.

-Minor defects of appearance, finish, or workmanship.

The different types of
defects first need to be classified as either A, B, C, or D. Once each defect
is classified, a weight is given to each class depending on its severity. The
most common weights used today are 100 for As, 50 for Bs, 10 for Cs, and 1 for
Ds.

Demerits are a defect of a product
multiplied by its weight.

Steps to Constructing a Demerit Control Chart

1. Calculate the number of demerits per sample. This is
done by counting the number of A, B, C, and D defects and multiplying that
number by the weight of each class. If there were 3 Class A defects then 3
would be multiplied by the Class A weight of 100 for a total of 300 demerits.
Add up the total demerits for each class to get the number of demerits per inspection
sample represented by d. This process is shown in the following formula:

2. Find the average number of demerits per unit, represented
by u, by taking the number of demerits per sample, d, and dividing by the
number of units in the sample, N.

u =
d / N

3. Find the average number of each class of defect per
unit. For Class A, take the total number of Class A defects in the sample and
divide by the number of units in the sample, N. Repeat for each class.

A = XA
/ N

4. Calculate the standard deviation through the following
formula.

σ = SqRt
((1002A + 502B
+ 102C + D)/N)

-where A is
the average number of Class A defects per unit

-N is the number of units in the sample

5. Calculate the control limits through the following
formulas.

Center
Line = =
100A
+ 50B
+ 10C
+ D

Upper Control Limit = + 3σ

Lower Control Limit
= - 3σ

6. Now that the center line and control limits have been
calculated, a control chart can be constructed. Information from future
inspections can be charted using these limits to monitor the performance of the
process and to insure that the process is in control.

Example

The easiest way to
learn to construct a demerit control chart is by following an example using
real numbers. For this example, the following information will be used.

Sample
size = 1500

Class of Defects

A

B

C

D

Number of Defects

2

5

12

13

First, calculate the total number of demerits in the sample
using the formula from step 1.

d = 100(2) + 50(5) + 10(12) + 13 = 583

Next, find the average number of demerits per unit.

u = 583/1500 = .39

Next, find the average number of each class of defect per
unit.

A =
2/1500 = .0013

B =
5/1500 = .0033

C
= 12/1500 =.008

D =
13/1500 = .009

Next, calculate the standard deviation.

σ = SqRt ((1002(.0013) + 502(.0033)
+ 102(.008) + .009)/N) = .12

Next, calculate the control limits.

Center
Line = 100(.0013) + 50(.0033) + 10(.008) + .009 =.384

UCL
= .384 + 3(.12) = .744

LCL
= .384 – 3(.12) = .024

Additional Information

A large quantity of information can be found
discussing control charts and the uses of control charts. However, compared to
regular control charts, not much has been published describing the demerit
control chart and the reasons for it. The best resources found are the
articles cited in the bibliography of this paper. A demerit chart is a type of
control chart, however, so a lot can be learned about them by reading what is
available about control charts and seeing how a demerit chart can relate.